rwhproductions
New member
- Joined
- Aug 19, 2017
- Messages
- 2
Hello everyone, this is my first time visiting this math forum; I have a query regarding the definite integration of a derivative or partial derivative which relates to a personal project I have been working on for a relatively long time.
I feel somewhat foolish asking the question as I am pretty sure it is a basic concept, but I digress. My question is this; is there a way to simplify the definite integral of a derivative or partial derivative of a multi-variable function? I am aware that the derivative of an indefinite integral leads to the original function, but I have been unable to find information about simplifying the definite integral of a derivative/partial derivative. I ask because the method I have been using has been resulting in constantly varying resulting and I'm hoping that simplifying the integral step will lead to stable results. Basically, I'm an attempting to use the average function value definite integral to find the average value of the partial derivative of a 3 variable function in relation to one specific variable.
My process of solving this problem up to this point has involved the use of the Mac grapher app to automate the process and is as follows; Grapher allows for the derivation of a function by simply placing "d/dx" in front of the function; I have been using this method because the partial derivative of the function is very long and complex.
There are 3 total variables in the function, two of which I have been giving specific values to and then changing each of them to record the relative change in the final integral in order to avoid using the complicated 3-variable partial derivative, the other variable is x which is what I wish to evaluate.
Firat I place the "d/dx" in front of the function to render the derivative, then put a set of parentheses around the whole thing and create an integral function in front of it using the range (a,b) I'm interested in finding, then I put a parenthesis around the integral and place the (1/(b-a)) expression in front of the integral.
This is the finished form I have been using to evaluate the average value of the derivative of the function in relation to x. I then change the definition of the two other variables and record them in different point sets to examine the change for each varying value. However, when I go back to check the results I have taken down for a pair of variables, I find the answers are slightly different from the values I have previously recorded.
My first thought was that the final expression was rather long and that something may have gone awry due to this fact, so I attempted to first record the result from integral and then multiply it by the (1/(b-a)) equation, which took much longer and in the end I still found that the results fluctuated. So now I assume that something must be going wrong in the programs automated "integral of the derivative" expressions and I'm hoping to find a way of simplifying the process in order to remove one of these automated functions.
My apologies in advance for this long and exhaustive post, thank you for your time and any assistance possible,
Rick
I feel somewhat foolish asking the question as I am pretty sure it is a basic concept, but I digress. My question is this; is there a way to simplify the definite integral of a derivative or partial derivative of a multi-variable function? I am aware that the derivative of an indefinite integral leads to the original function, but I have been unable to find information about simplifying the definite integral of a derivative/partial derivative. I ask because the method I have been using has been resulting in constantly varying resulting and I'm hoping that simplifying the integral step will lead to stable results. Basically, I'm an attempting to use the average function value definite integral to find the average value of the partial derivative of a 3 variable function in relation to one specific variable.
My process of solving this problem up to this point has involved the use of the Mac grapher app to automate the process and is as follows; Grapher allows for the derivation of a function by simply placing "d/dx" in front of the function; I have been using this method because the partial derivative of the function is very long and complex.
There are 3 total variables in the function, two of which I have been giving specific values to and then changing each of them to record the relative change in the final integral in order to avoid using the complicated 3-variable partial derivative, the other variable is x which is what I wish to evaluate.
Firat I place the "d/dx" in front of the function to render the derivative, then put a set of parentheses around the whole thing and create an integral function in front of it using the range (a,b) I'm interested in finding, then I put a parenthesis around the integral and place the (1/(b-a)) expression in front of the integral.
This is the finished form I have been using to evaluate the average value of the derivative of the function in relation to x. I then change the definition of the two other variables and record them in different point sets to examine the change for each varying value. However, when I go back to check the results I have taken down for a pair of variables, I find the answers are slightly different from the values I have previously recorded.
My first thought was that the final expression was rather long and that something may have gone awry due to this fact, so I attempted to first record the result from integral and then multiply it by the (1/(b-a)) equation, which took much longer and in the end I still found that the results fluctuated. So now I assume that something must be going wrong in the programs automated "integral of the derivative" expressions and I'm hoping to find a way of simplifying the process in order to remove one of these automated functions.
My apologies in advance for this long and exhaustive post, thank you for your time and any assistance possible,
Rick
